Certainly we can almost search all information from the Internet, yet all we retrieve is just pictures and texts. While in a museum, one see real objects, such as a Chinese ancient porcelain pot, at a very close distance. Comparing with what is seen on the Internet, this is much more precious first-hand experience. Also, museums and galleries are the best place to protect those precious antiques, which may be damaged without proper and professional preservation. For instance, without moderate temperature and humidity, a piece of silk clothes in the Ming dynasty would loss its color gradually and even break into pieces. Moreover, many museums hold special exhibitions on specific topics regularly, with experts invited to give lectures to the public. Such experience of interaction is also superior to just surfing on the Internet.
Some famous museums and galleries can even become cultural symbols of a city, which attract tourists to visit. They are the places where travellers can learn about local culture and history. The National Gallery in London is a case in point.
I admit that, in many cases, it is more convenient and cheaper to reckon on computer and the Internet, than to go to museums and galleries. However I still believe that there is a gread demand for museums and art galleries.